In this paper, we provide an algorithm to convert the third-order nonlinear evolution equations to regular higher-order partial differential equations near movable singularities. Therefore, the Cauchy-Kowalevski theorem is always applicable. As a result, we always have a routine conceptual proof of the convergence of the Laurent series obtained from the Painlevé test. Copyright © 2021 Hikari Ltd.
CitationYee, T. L. (2021). A method of proving the convergence of the formal Laurent series solutions of nonlinear evolution equations. International Journal of Mathematical Analysis, 15(1), 1-21. doi: 10.12988/ijma.2021.912133
- Laurent series solution